In literature:
Sometimes the notch is very slight.
"Studies of American Fungi. Mushrooms, Edible, Poisonous, etc." by George Francis Atkinson
Now push to the right one notch the pointer which reduces the size of the hole.
"If You Don't Write Fiction" by Charles Phelps Cushing
If the sticks vary in size, the larger ones should be notched down on the transom so as to bring the tops in the same plane.
"Manual of Military Training" by James A. Moss
They mounted and rode toward the notch in the hills that had been pointed out to the ranger.
"Brand Blotters" by William MacLeod Raine
The breeze came pouring over the prairie from the far southwest where the purple notches stood sentinel.
"Winning the Wilderness" by Margaret Hill McCarter
The sapling, jarred out of the notch, springing upward!
"David and the Phoenix" by Edward Ormondroyd
In the bush, I was to keep my eye on the notches in the trees, and follow them.
"The Story of John G. Paton" by James Paton
Notch about four or five back logs with the plain, rounded notch already described and illustrated by Fig.
"Shelters, Shacks and Shanties" by D.C. Beard
Ward's literary efforts, along about that time, consisted of cutting notches in the window-sill beside his bunk.
"The Ranch at the Wolverine" by B. M. Bower
When breakfast was over, Mrs McQueen brought a stick with notches cut in it and gave it to Mr McQueen.
"The Irish Twins" by Lucy Fitch Perkins
Two blows of the light belt ax made a notch into which the small steel trap fitted perfectly.
"Connie Morgan in the Fur Country" by James B. Hendryx
There Warrenton is to show me how to notch arrows and pick a courtly bow.
"Robin Hood" by Paul Creswick
She leaned down again and called once more into the stallion's ear and once more the note rose a notch.
"Tharon of Lost Valley" by Vingie E. Roe
There are six notches on the hilt of his 'gun,' if you count the two little ones he nicked for his brace of Utes.
"Out of the Depths" by Robert Ames Bennet
He took the bow, and fitting an arrow to the notch, took careful aim and let fly.
"Boys and Girls Bookshelf (Vol 2 of 17)" by Various
As for safety, the mouth of this notch could be made a perfect fort of, if we had to quit mining and go to fighting.
"Two Arrows" by William O. Stoddard
Seeds adherent, one to five, large, deeply notched, with enlarged neck, brown.
"Manual of American Grape-Growing" by U. P. Hedrick
All this frightful swinging mass was held only by one chain, which was itself only kept in position by a filed notch.
"Toilers of the Sea" by Victor Hugo
At any rate, Colonel Kracker reduced his pace another notch, as if in answer to an unspoken challenge.
"The Boy Scouts in the Rockies" by Herbert Carter
The notch was dead ahead.
"A Yankee Flier with the R.A.F." by Rutherford G. Montgomery
***
In poetry:
He carved a flute of elder green,
And notched it well and true,
Then pursed his lips and puffed his cheeks
And merrily he blew.
"Pan In The Orchard" by Maurice Thompson
We need not waste our school-boy art
To gild this notch of Time;--
Forgive me if my wayward heart
Has throbbed in artless rhyme.
"At A Birthday Festival" by Oliver Wendell Holmes
Year by year, like milestones placed,
Mark the record Friendship traced.
Prisoned in the walls of time
Life has notched itself in rhyme.
"Programme" by Oliver Wendell Holmes
Not man nor demigod could put together
The scraps of rusted reverie, the wheels
Of notched tin platitudes concerning weather,
Perfume, politics, and fixed ideals.
"Sonnet : To Eva" by Sylvia Plath
Of an old tree, whose notched and scanty leaves
Repeat the tale of woe,
And quiver day and night,
Till the snow cometh, and a cold shroud weaves,
Whiter than that below.
"The House Of Youth" by Elizabeth Drew Barstow Stoddard
Genius, that wind-worn reed, unsightly, rude,
Notched by some strong, untutored artisan;
That golden lyre, that lute of jeweled wood,
That syrinx blown by furry lips of Pan!
"To A Realist" by Maurice Thompson
In news:
Ambarella's IPO Notches Slim Gain After Price Cut .
Prince Albert, SK- Tri-City persevered and notched their first comeback win of the season.
DeMOTTE — Raelynn LaFrance notched a hat trick,and Jami Patterson added a pair of tallies as Argos advanced to the Covenant Christian Soccer Sectional final with a 5-0 shutout of Rensselaer Central Thursday.
Square Lake Diner takes fare we know up a notch.
A serene wellness center in Soho housing nine holistic practitioners, all offering top-notch service.
The lessons read like those from UC Berkeley, Wellesley or another top-notch liberal arts college.
Top notch from top down.
Yankees' Melky Cabrera notches four RBIs in ALCS Game 4, breaking… (Sipkin/News ).
Islander notches another round of golf better than his age.
He notched one sack for a 2-yard loss and forced a fumble on it.
The Mets notched five hits and walked four times.
This is the 10th Anniversary batch, and things have been kicked up a notch.
To make installing the C-notch easier, a scraper and paint thinner was used to remove the thick, factory undercoat from that area of the frame.
Model and reality television host Heidi Klum is adding another notch to her resume -- this time designing baby wear and accessories for the Babies R Us chain.
It's one of the hottest spots on the Central Coast for a good seafood dinner, but Tuesday, it's stepping it up a notch or two to save lives as well.
***
In science:
Then ι(β ) is obtained by tagging α plain at a and notched at b.
Positivity for cluster algebras from surfaces
So given a tagged triangulation T, let us perform such changes at every puncture where all ends of T are notched.
Positivity for cluster algebras from surfaces
Given a surface (S, M ) with a puncture p and a tagged arc γ, we let both γ (p) and γ p denote the arc obtained from γ by changing its notching at p. (So if γ is not incident to p, γ (p) = γ .) If p and q are two punctures, we let γ (pq) denote the arc obtained from γ by changing its notching at both p and q .
Positivity for cluster algebras from surfaces
If γ has an endpoint at a puncture, then Lγ spirals into a: counterclockwise if γ is tagged plain at a, and clockwise if it is notched.
Positivity for cluster algebras from surfaces
We present three slightly different formulas, based on whether the cluster variable corresponds to a tagged arc with 0, 1, or 2 notched ends.
Positivity for cluster algebras from surfaces
In the case of γ (p), an arc between points p and q with a single notch at p, we build the graph GT ◦, ℓp associated to the loop ℓp such that ι(ℓp ) = γ (p) .
Positivity for cluster algebras from surfaces
In the case of γ (pq), an arc between points p and q which is notched at both p and q, we build the two graphs GT ◦, ℓp and GT ◦, ℓq associated to ℓp and ℓq .
Positivity for cluster algebras from surfaces
This is relevant to our formula for the doubly-notched loop, see Remark 4.22.
Positivity for cluster algebras from surfaces
Cluster expansion formulas for tagged arcs with notches.
Positivity for cluster algebras from surfaces
We now consider cluster variables of tagged arcs which have a notched end.
Positivity for cluster algebras from surfaces
The following remark shows that if we want to compute the Laurent expansion of a cluster variable associated to a tagged arc notched at p, with respect to a tagged triangulation T, there is no loss of generality in assuming that all arcs in T are tagged plain at p.
Positivity for cluster algebras from surfaces
Note that if there is no tagged arc in T which is notched at p, then there is no loop in T ◦ cutting out a once-punctured monogon around p.
Positivity for cluster algebras from surfaces
Similarly, if p and q are punctures and we are interested in computing the Laurent expansion of xγ (pq) with respect to T, we may assume that no tagged arc in T is notched at either p or q (equivalently, there are no loops in T ◦ cutting out once-punctured monogons around p or q).
Positivity for cluster algebras from surfaces
Deﬁnition 4.12 (Crossing monomials for tagged arcs with notches ).
Positivity for cluster algebras from surfaces
If p is a puncture, and γ (p) is a tagged arc with a notch at p but tagged plain at its other end, we deﬁne the associated crossing monomial as = cross(T ◦, γ ) Yτ cross(T ◦, ℓp) cross(T ◦, γ ) where the product is over all ends of arcs τ of T ◦ that are incident to p.
Positivity for cluster algebras from surfaces
***